In this paper we introduce robust and stochastically weighted sum approaches to deterministic and stochastic multi-objective optimization. The robust weighted sum approach minimizes the worst case weighted sum of objectives over a given weight region. We study the reformulations of the robust weighted sum problem under different definitions of deterministic weight regions. We next introduce … Read more
Energy supply routes to a given TIAM region (say E.U.) are subject to randomness, resulting in partial or total closure of a route (corridor). For instance: a pipeline may be subject to technical problems that reduce its capacity. Or, oil supply by tanker may be reduced for political reasons or because of equipment mishaps at … Read more
We consider the capacity planning of telecommunication networks with linear investment costs and uncertain future traffic demands. Transmission capacities must be large enough to meet, with a high quality of service, the range of possible demands, after adequate routings of messages on the created network. We use the robust optimization methodology to balance the need … Read more
We develop tractable semidefinite programming (SDP) based approximations for distributionally robust individual and joint chance constraints, assuming that only the first- and second-order moments as well as the support of the uncertain parameters are given. It is known that robust chance constraints can be conservatively approximated by Worst-Case Conditional Value-at-Risk (CVaR) constraints. We first prove … Read more
Stochastic programming provides a versatile framework for decision-making under uncertainty, but the resulting optimization problems can be computationally demanding. It has recently been shown that, primal and dual linear decision rule approximations can yield tractable upper and lower bounds on the optimal value of a stochastic program. Unfortunately, linear decision rules often provide crude approximations … Read more
We show that a first order problem can approximate solutions of a robust optimization problem when the uncertainty set is scaled, and explore further properties of this first order problem. Article Download View First order dependence on uncertainty sets in robust optimization
We address bilevel programming problems when the derivatives of both the upper and the lower level objective functions are unavailable. The core algorithms used for both levels are trust-region interpolation-based methods, using minimum Frobenius norm quadratic models when the number of points is smaller than the number of basis components. We take advantage of the … Read more
This paper presents and studies several models for multi-criterion budget allocation problems under uncertainty. We start by introducing a robust weighted objective model, which is developed further using the concept of stochastic dominance to incorporate risk averseness of the decision maker. A budget minimization variant of this model is also presented. We use a Sample … Read more
Inferences need to be drawn in biological systems using experimental multivariate data. The number of samples collected in many such experiments is small, and the data is noisy. We present and study the performance of a robust optimization (RO) model for such situations. We adapt this model to generate a minimum and a maximum estimation … Read more
We propose a novel robust optimization technique, which is applicable to nonconvex and simulation-based problems. Robust optimization finds decisions with the best worst-case performance under uncertainty. If constraints are present, decisions should also be feasible under perturbations. In the real-world, many problems are nonconvex and involve computer-based simulations. In these applications, the relationship between decision … Read more